Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systems

We consider an autonomous dynamical system coming from a coupled system in cascade where the uncoupled part of the system satisfies that the solutions comes from −∞ and goes to ∞ to equilibrium points, and where the coupled part generates asymptotically a gradient-like nonlinear semigroup. Then, the...

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Detalles Bibliográficos
Autores: Aragão Costa, Eder Ritis, Carvalho, Alexandre Nolasco, Marín Rubio, Pedro, Planas, Gabriela
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2013
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/84122
Acceso en línea:https://hdl.handle.net/11441/84122
Access Level:acceso abierto
Palabra clave:Dynamical system
Nonlinear semigroup
Attractor
Gradient-like semigroup
Łojasiewicz-Simon inequality
Descripción
Sumario:We consider an autonomous dynamical system coming from a coupled system in cascade where the uncoupled part of the system satisfies that the solutions comes from −∞ and goes to ∞ to equilibrium points, and where the coupled part generates asymptotically a gradient-like nonlinear semigroup. Then, the complete model is proved to be also gradient-like. The interest of this extension comes, for instance, in models where a continuum of equilibrium points holds, and for example a Lojasiewicz-Simon condition is satisfied. Indeed, we illustrate the usefulness of the theory with several examples.